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bundles / scipy latest / scipy / signal / _signaltools / correlate

function

`scipy.signal._signaltools:correlate`

source: /scipy/signal/_signaltools.py :104

Signature

def correlate ( in1 , in2 , mode = full , method = auto )

Summary

Cross-correlate two N-dimensional arrays.

Extended Summary

Cross-correlate in1 and in2, with the output size determined by the mode argument.

Parameters

in1 : array_like

First input.

in2 : array_like

Second input. Should have the same number of dimensions as in1.

mode : str {'full', 'valid', 'same'}, optional

A string indicating the size of the output:

full: The output is the full discrete linear cross-correlation of the inputs. (Default)
valid: The output consists only of those elements that do not rely on the zero-padding. In 'valid' mode, either in1 or in2 must be at least as large as the other in every dimension.
same: The output is the same size as in1, centered with respect to the 'full' output.

method : str {'auto', 'direct', 'fft'}, optional

A string indicating which method to use to calculate the correlation.

direct: The correlation is determined directly from sums, the definition of correlation.
fft: The Fast Fourier Transform is used to perform the correlation more quickly (only available for numerical arrays.)
auto: Automatically chooses direct or Fourier method based on an estimate of which is faster (default). See convolve Notes for more detail.
versionadded 0.19.0

Returns

correlate : array: An N-dimensional array containing a subset of the discrete linear cross-correlation of in1 with in2.

Notes

The correlation z of two d-dimensional arrays x and y is defined as

z[...,k,...] = sum[..., i_l, ...] x[..., i_l,...] * conj(y[..., i_l - k,...])

This way, if x and y are 1-D arrays and z = correlate(x, y, 'full') then

z [k] = l = 0 \sum N - 1 x_{l} y_{l - k}^{*}

for $k = - (M - 1), \dots, (N - 1)$ , where $N$ is the length of x, $M$ is the length of y, and $y_{m} = 0$ when $m$ is outside the valid range $[0, M - 1]$ . The size of $z$ is $N + M - 1$ and $y^{*}$ denotes the complex conjugate of $y$ .

method='fft' only works for numerical arrays as it relies on fftconvolve. In certain cases (i.e., arrays of objects or when rounding integers can lose precision), method='direct' is always used.

When using mode='same' with even-length inputs, the outputs of correlate and correlate2d differ: There is a 1-index offset between them.

Array API Standard Support

correlate has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ⛔                   
JAX                   ✅                     ✅                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

CuPy does not support inputs with ndim>1 when method="auto" but does support higher dimensional arrays for method="direct" and method="fft".

See dev-arrayapi for more information.

Examples

Implement a matched filter using cross-correlation, to recover a signal that has passed through a noisy channel.

import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
rng = np.random.default_rng()

✓

sig = np.repeat([0., 1., 1., 0., 1., 0., 0., 1.], 128)
sig_noise = sig + rng.standard_normal(len(sig))
corr = signal.correlate(sig_noise, np.ones(128), mode='same') / 128

✓

clock = np.arange(64, len(sig), 128)
fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, sharex=True)

✓

ax_orig.plot(sig)
ax_orig.plot(clock, sig[clock], 'ro')
ax_orig.set_title('Original signal')
ax_noise.plot(sig_noise)
ax_noise.set_title('Signal with noise')
ax_corr.plot(corr)
ax_corr.plot(clock, corr[clock], 'ro')
ax_corr.axhline(0.5, ls=':')
ax_corr.set_title('Cross-correlated with rectangular pulse')

✗

ax_orig.margins(0, 0.1)
fig.tight_layout()
plt.show()

✓

Compute the cross-correlation of a noisy signal with the original signal.

x = np.arange(128) / 128
sig = np.sin(2 * np.pi * x)
sig_noise = sig + rng.standard_normal(len(sig))
corr = signal.correlate(sig_noise, sig)
lags = signal.correlation_lags(len(sig), len(sig_noise))
corr /= np.max(corr)

✓

fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, figsize=(4.8, 4.8))

✓

ax_orig.plot(sig)
ax_orig.set_title('Original signal')
ax_orig.set_xlabel('Sample Number')
ax_noise.plot(sig_noise)
ax_noise.set_title('Signal with noise')
ax_noise.set_xlabel('Sample Number')
ax_corr.plot(lags, corr)
ax_corr.set_title('Cross-correlated signal')
ax_corr.set_xlabel('Lag')

✗

ax_orig.margins(0, 0.1)
ax_noise.margins(0, 0.1)
ax_corr.margins(0, 0.1)
fig.tight_layout()
plt.show()

✓

`scipy.signal._signaltools:correlate`

Signature

Summary

Extended Summary

Parameters

Returns

Notes

Examples

See also

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